5 answers

From what research I've read in this thread, it appears that the formula for an orbit is:

r = A * m * v^2 / (sqrt (Vmax^2 - v^2) * 10^6)

r = Orbital Radius

A = Agility

m = ship mass (in kg)

VMax = maximum velocity for the ship

v = orbit velocity for the ship

Realize that you're solving for radius here rather than velocity. Note that you will not be traveling at maximum velocity around the object (that would divide by zero and cause the universe to explode).

The orbit velocity for the ship has some trig that I'm not entirely comfortable with.

Closed form solutions to your question can be computed from these notes on the mathematics of ship motion in EVE-Online Chapter 1. I was unaware of the thread on EVE-O forums that discusses similar results, motion thread, until today. Fortunately, my link describes how you can also solve for the radius of the orbit as well as the velocity. Perhaps more can be written about this in the future when I get time...

Just to take this out of the theoretical and give you an in-game example: if you have a Crow with a max speed (in a straight line) of ~4800m/s, and set the crow to orbit at max speed at 17km, you will generally end up in an orbit just on the outer edge of 20km at an actual speed of roughly ~4200m/s. If you set the Crow to orbit at 500m at full speed, you will end up in an orbit of around 5000m at around 1000m/s (but my memory is hazy on this one, so please correct me if wrong). Again, this is very generalized, but should give you and idea of some parameters to start experimenting with. Now it can chance quite a bit based on fitting (nanofibers, inertials, rigs) and navigation skills.

Conversely, in a Taranis set to orbit at 500m using an AB with a max speed of 1400m/s, the orbit will end up at ~3500m at around 800m/s.

So how are those values calculated, do you think? If I set a radius and a speed, the ship will never match those values unless I pick a large orbit and/or small speed. Better still, how would I calculate that the orbit will be elliptical instead of circular?

Orbit will settle to circular around unmoving object. If you set the speed (manually) for your ship to ~1 m/s, your orbit should be spot on… Or if you 0 the mass (fly a pod for the closest approximation).

@YuriPup – there is. However, solving 3d vector problems and differentials isn’t trivial for undergrad level college math. It is further complicated by the question of “is the subject at rest or in motion?” One will get different answers for the tightest orbit (when orbiting a ship in motion you sometimes have to play ‘catch up’ to it). Two threads on orbit math I’ve found – http://tinyurl.com/27yskmx and http://tinyurl.com/2cxejdk — Still trying to get my head around some of them.